Subgroups — C₂×C₉⋊(D₁₃₁⋊C₅) #37556042

Order 23580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉⋊(D₁₃₁⋊C₅)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊(D₁₃₁⋊C₅)	—	3	1	no	maximal
4	C₉×C₁₃₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₁₇₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃⋊(D₁₃₁⋊C₅)	—	3	2	no	—
7	C₂×C₃×C₁₃₁⋊C₅	D₃	1	1	yes	characteristic
8	C₂×D₁₃₁⋊C₅	—	9	1	no	Hall
9	D₁₁₇₉	C₂×C₅	1	2	yes	complemented
10	C₂×C₉×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₁₃₁⋊C₅	C₂×D₃	1	1	yes	characteristic
12	C₂×D₃₉₃	—	3	1	no	—
13	C₂×C₁₃₁⋊C₅	D₉	1	1	yes	characteristic, complemented
14	D₁₃₁⋊C₅	—	9	2	no	—
15	C₉×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₃₁	C₅×D₃	1	1	yes	characteristic
17	D₃₉₃	—	3	2	no	—
18	C₁₃₁⋊C₅	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₃₁	—	9	1	no	Hall
20	C₃×C₁₃₁	C₂×C₅×D₃	1	1	yes	characteristic
21	C₂×C₁₃₁	C₅×D₉	1	1	yes	characteristic, complemented
22	D₁₃₁	—	9	2	no	—
23	C₂×C₅×D₉	—	131	1	no	maximal, Hall
24	C₁₃₁	C₂×C₅×D₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅×C₉	—	131	1	no	—
26	C₅×D₉	—	131	2	no	—
27	C₂×C₅×D₃	—	393	1	no	—
28	C₅×C₉	—	131	1	no	Hall
29	C₂×D₉	—	131	1	no	Hall
30	C₂×C₃×C₅	—	131	1	no	—
31	C₅×D₃	—	393	2	no	—
32	C₂²×C₅	—	1179	1	no	Hall
33	C₂×C₉	D₁₃₁⋊C₅	1	1	yes	characteristic, complemented
34	D₉	—	131	2	no	—
35	C₃×C₅	—	131	1	no	—
36	C₂×D₃	—	393	1	no	—
37	C₂×C₅	—	131	1	no	—
38	C₂×C₅	—	1179	2	no	—
39	C₉	C₂×D₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	C₃⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic
41	D₃	—	393	2	no	—
42	C₅	—	131	1	no	Sylow
43	C₂²	—	1179	1	no	Sylow
44	C₃	C₂×C₃⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic
45	C₂	—	1179	2	no	—
46	C₂	C₉⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₉⋊(D₁₃₁⋊C₅)
commutator, cosocle, hypocenter	C₉×C₁₃₁	C₂²×C₅
Frattini	C₃	C₂×C₃⋊(D₁₃₁⋊C₅)
Fitting	C₂×C₉×C₁₃₁	C₂×C₅
socle	C₂×C₃×C₁₃₁	C₅×D₃
LCS	G ▷ C₉×C₁₃₁
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₉⋊(D₁₃₁⋊C₅)	C₂	direct (N × H)
2. C₂×C₉×C₁₃₁⋊C₅	C₂	semidirect
4. C₉×C₁₃₁⋊C₅	C₂²	semidirect
5. C₂×D₁₁₇₉	C₅	semidirect
9. D₁₁₇₉	C₂×C₅	semidirect
10. C₂×C₉×C₁₃₁	C₂×C₅	semidirect
13. C₂×C₁₃₁⋊C₅	D₉	semidirect
15. C₉×C₁₃₁	C₂²×C₅	semidirect
18. C₁₃₁⋊C₅	C₂×D₉	semidirect
21. C₂×C₁₃₁	C₅×D₉	semidirect
24. C₁₃₁	C₂×C₅×D₉	semidirect
33. C₂×C₉	D₁₃₁⋊C₅	semidirect
39. C₉	C₂×D₁₃₁⋊C₅	semidirect
46. C₂	C₉⋊(D₁₃₁⋊C₅)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉⋊(D₁₃₁⋊C₅)	2
C₂×C₉×C₁₃₁⋊C₅	2
C₂×C₃⋊(D₁₃₁⋊C₅)	3
C₂×D₁₁₇₉	5
C₂×C₅×D₉	131

Subgroups — C2×C9⋊(D131⋊C5) #37556042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉⋊(D₁₃₁⋊C₅) #37556042